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arXiv · 2607.07835

Super-Logarithmic Entanglement Scaling in a Monitored Superconducting Chain

Rui-Jing Guo·Zhi-Yuan Wei
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Abstract

We study the entanglement dynamics of a one-dimensional spinful $s$-wave superconductor subjected to local continuous measurements. In the rare-measurement regime, we derive a replicated Keldysh non-linear sigma model (NLSM) to describe the steady-state entanglement. Within this field-theoretic framework, the interplay between measurement dephasing and superconducting pairing constrains the low-energy, long-wavelength fluctuations to an $\mathrm{SO(R)}$ target manifold. A one-loop renormalization-group analysis shows that the theory develops a weak-anti-localization flow, stabilizing a critical phase with super-logarithmic scaling of the steady-state entanglement. Our field-theoretic results explain the numerical evidence reported in the companion Letter [arXiv:2604.04375] and demonstrate that such a critical phase can emerge in a one-dimensional topologically trivial superconductor without relying on topological protection.

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Rui-Jing Guo, Zhi-Yuan Wei. 2026-07-08. Super-Logarithmic Entanglement Scaling in a Monitored Superconducting Chain. https://arxiv.org/abs/2607.07835

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